An operator algebra associated with a pair of intersecting manifolds

TL;DR

This paper constructs an operator algebra from intersecting manifolds using pseudodifferential and boundary operators, defining its generators and symbols, and establishing a composition formula.

Contribution

It introduces a new operator algebra associated with intersecting manifolds, detailing its generators, symbols, and composition rules.

Findings

The algebra has 18 types of additive generators.

Symbols for the algebra's operators are explicitly defined.

A composition formula for the operators is established.

Abstract

Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that this algebra has 18 types of additive generators. Then we define the symbols of the operators in this algebra and obtain the composition formula.